On one of winter's coldest days, local officials met to discuss a problem that grows with summer's heat.

"It sounds like some kind of monster that is taking over us," said Martha V. Pennino (D-Centreville), vice chairman of the Fairfax County Board of Supervisors. "I thought we could send the dastardly stuff to Libya."

Pennino was talking about hydrilla, the aquatic weed that grows like kudzu in a warm Potomac River. Almost unheard of until two years ago, hydrilla since has spread over 1,900 acres of the river, and, according to the Army Corps of Engineers, is expected to cover a whopping 36,000 acres by 1995.

After a year of discussing chemicals, dredging -- even 500-watt lamps -- as ways to eliminate the thick weed, area officials endorsed yesterday the Corps plan to mow down the green weed with a floating mechanical harvester.

The harvester, about the size of a pickup truck, will cut off hydrilla six feet below the surface and unclog waterways, marinas and boat slips, Corps spokesmen said. The first mowing in the area between Mount Vernon and Chain Bridge is scheduled to begin in June.

But still, the question of who will pay the estimated $276,000 annual cost over the next decade to cut the 290 acres of hydrilla that clogs key channels is a sore one.

Attending yesterday's meeting of the Metropolitan Washington Council of Governments, officials from Fairfax, Arlington and Prince William counties and the city of Alexandria said they would pressure the 1986 Virginia General Assembly to pay for what they believed was a state problem.

Many were angered by a recently released memo from the Virginia Commerce and Resources office that said the state believes hydrilla is a "highly localized" problem and should be funded by those directly affected.

Maryland and District officials have indicated they will pick up their hydrilla-mowing costs.

The Corps' cost-sharing plan, which likely will be approved in final form this spring after the funding question is resolved, calls for the federal government to pay 70 percent of the cost, or $193,200. Maryland would contribute $38,900, Virginia $34,800 and the District, $9,100.

"The Commonwealth of Virginia will always shuck off the cost on the localities whenever possible," said Fairfax Supervisor Nancy K. Falck (R-Dranesville). "Even though it is only modest costs, it's the principle. It's one more time the state didn't honor their responsibility."

Prince William County Supervisor Kathleen K. Seefeldt (D-Occoquan) said her board has already passed a resolution asserting the state's responsibility to cover hydrilla removal costs.

But one official thought there might be a way to make money on the project.

"I don't want to be corny," said Rose Crenca, Montgomery County Council member, "but I think we are missing the boat. This weed has a lot of protein in it . . . . I've eaten seaweed and sushi. We may have a good thing here. I'm serious."

No one responded.